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arXiv · 1605.05277

Tropical and non-Archimedean limits of degenerating families of volume forms

Sébastien Boucksom·Mattias Jonsson
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Abstract

We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theoretic version of a conjecture by Kontsevich--Soibelman and Gross--Wilson, bearing on maximal degenerations of Calabi--Yau manifolds.

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Sébastien Boucksom, Mattias Jonsson. 2016-12-20. Tropical and non-Archimedean limits of degenerating families of volume forms. https://arxiv.org/abs/1605.05277

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